A simple gear train is designed to transfer a constant angular velocity to a shaft which drives the crank in a four-bar crank-slider mechanism. The gear and the pin- ion in the gear train have 90 and 23 teeth, respectively. The gear has a constant an- gular velocity of (1.25t) rad/s CCW. The slider is a piston that compresses air in- side a cylinder. The compressed air acts like a spring that exerts a restoring force to the slider. This equivalent spring has a stiffness of 2500 N/m and original length of 15 cm. Calculate the torque for the gear at the instant shown. The crank rotates with the same angular velocity of the shaft it is mounted on. Pay attention to the units. Given: Link 2, a = 7.5 cm Link 3, b = 25 cm 02 = 124.228° Horizontal length of the slider = 4 cm D= 31 cm R12 = 2.5 cm (Distance between CG2 and O2) R23 = 6.25 cm (Distance between CG3 and A) H = 0.15 m2 = 0.5 kg m; = 1 kg m4 = 2 kg IG2 = 2 kg.cm? IG3 = 4 kg.cm? CG3 Gear A Equivalent Spring 4 cm CG2 a Wg 02 D=31 cm Pinion

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Question
A simple gear train is designed to transfer a constant angular velocity to a shaft
which drives the crank in a four-bar crank-slider mechanism. The gear and the pin-
ion in the gear train have 90 and 23 teeth, respectively. The gear has a constant an-
gular velocity of (1.257) rad/s CCW. The slider is a piston that compresses air in-
side a cylinder. The compressed air acts like a spring that exerts a restoring force to
the slider. This equivalent spring has a stiffness of 2500 N/m and original length of
15 cm. Calculate the torque for the gear at the instant shown. The crank rotates
with the same angular velocity of the shaft it is mounted on. Pay attention to the
units.
Given:
Link 2, a = 7.5 cm
Link 3, b = 25 cm
02 = 124.228°
Horizontal length of the slider = 4 cm
D= 31 cm
R12 = 2.5 cm (Distance between CG2 and O2)
R23 = 6.25 cm (Distance between CG; and A)
u = 0.15
m2 = 0.5 kg
m; = 1 kg
m4 = 2 kg
Ic2 = 2 kg.cm?
IG3 = 4 kg.cm?
CG3
A
Equivalent
Spring
Gear
CG2
4 cm
Wg
02
d
D=31 cm
Pinion
Transcribed Image Text:A simple gear train is designed to transfer a constant angular velocity to a shaft which drives the crank in a four-bar crank-slider mechanism. The gear and the pin- ion in the gear train have 90 and 23 teeth, respectively. The gear has a constant an- gular velocity of (1.257) rad/s CCW. The slider is a piston that compresses air in- side a cylinder. The compressed air acts like a spring that exerts a restoring force to the slider. This equivalent spring has a stiffness of 2500 N/m and original length of 15 cm. Calculate the torque for the gear at the instant shown. The crank rotates with the same angular velocity of the shaft it is mounted on. Pay attention to the units. Given: Link 2, a = 7.5 cm Link 3, b = 25 cm 02 = 124.228° Horizontal length of the slider = 4 cm D= 31 cm R12 = 2.5 cm (Distance between CG2 and O2) R23 = 6.25 cm (Distance between CG; and A) u = 0.15 m2 = 0.5 kg m; = 1 kg m4 = 2 kg Ic2 = 2 kg.cm? IG3 = 4 kg.cm? CG3 A Equivalent Spring Gear CG2 4 cm Wg 02 d D=31 cm Pinion
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